Boundary Conformal Field Theories, Limit Sets of Kleinian Groups and Holography

TL;DR

This paper explores the mathematical and physical connections between boundary conformal field theories, hyperbolic geometry, and holography, extending previous results to higher dimensions and clarifying theoretical objections.

Contribution

It generalizes existing results on hyperbolic manifolds and conformal field theories, demonstrating the feasibility of higher-dimensional extensions and resolving prior objections.

Findings

Extended work of Belavin, Polyakov, and Zamolodchikov to higher dimensions.

Reproduced and generalized results on hyperbolic manifolds and discrete groups.

Demonstrated the plausibility of higher-dimensional holographic correspondences.

Abstract

In this paper,based on the available mathematical works on geometry and topology of hyperbolic manifolds and discrete groups, some results of Freedman et al (hep-th/9804058) are reproduced and broadly generalized. Among many new results the possibility of extension of work of Belavin, Polyakov and Zamolodchikov to higher dimensions is investigated. Known in physical literature objections against such extension are removed and the possibility of an extension is convincingly demonstrated.